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Journal of Convex Analysis 14 (2007), No. 3, 607--619
Copyright Heldermann Verlag 2007



Twisted Convex Hulls in the Heisenberg Group

Andrea Calogero
Dip. di Statistica, UniversitÓ di Milano-Bicocca, Via Bicocca degli Arcimboldi 8, 20126 Milano, Italy
andrea.calogero@unimib.it

Giovanna Carcano
Dip. di Metodi Quantitativi per le Scienze Economiche ed Aziendali, UniversitÓ di Milano-Bicocca, Piazza Ateneo Nuovo 1, 20126 Milano, Italy
giovanna.carcano@unimib.it

Rita Pini
Dip. di Metodi Quantitativi per le Scienze Economiche ed Aziendali, UniversitÓ di Milano-Bicocca, Piazza Ateneo Nuovo 1, 20126 Milano, Italy
rita.pini@unimib.it



We define and investigate the notion of twisted convex hull for a subset of the Heisenberg group H. We show that, while the twisted convex hull of two points is always a bounded set, the twisted convex hull of n > 2 points is, in general, an unbounded prism, with edges parallel to the t axis. These results shed some light on the twisted convex subsets of H in particular, we give a characterization of their interior.

Keywords: Heisenberg group, twisted convex combination, twisted convex hull, horizontal planes.

MSC: 52A01, 53C17, 22E25

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